Square roots question: (square root of 5 + square root of 2)^2

[Acecustis]

Please help solve. I'm sure this is simple but I feel like I'm doing something wrong.

(square root of 5 + square root of 2)²


Both numbers are not under one radical but separate radicals (not sure if that matters).

I'm getting 7 for my answer.
Square root of 5 squared = 5
Square root of 2 squared = 2

5+2 = 7

 

[Denis]

(square root of 5 + square root of 2)²

Both numbers are not under one radical but separate radicals (not sure if that matters).

I'm getting 7 for my answer.
Square root of 5 squared = 5
Square root of 2 squared = 2

5+2 = 7

Use something SIMPLER, like:
(√4 + √9)^2
= (2 + 3)^2
= 5^2
=25

Now ask your question "clearly"...thanks.

 

[HallsofIvy]

Yes, that is wrong. $\displaystyle (a+ b)^2$ is NOT equal to $\displaystyle a^2+ b^2$! Instead $\displaystyle (a+ b)^2= (a+ b)(a+ b)= a(a+ b)+ b(a+ b)$
$\displaystyle = a^2+ ab+ ab+ b^2= a^2+ 2ab+ b^2$ (I'll bet you've seen that before and forgot it!).

$\displaystyle (\sqrt{5}+ \sqrt{2})^2= (\sqrt{5})^2+ 2(\sqrt{5})(\sqrt{2})+ (\sqrt{2})^2$
$\displaystyle = 5+ 2\sqrt{(2)(5)}+ 2= 7+ 2\sqrt{10}$.

As a check, look at the approximate calculator values:
$\displaystyle \sqrt{5}$ is approximately 2.236 and $\displaystyle \sqrt{2}$ is approximately 1.414. $\displaystyle \sqrt{5}+ \sqrt{2}= 2.236+ 1.414= 3.650$ so $\displaystyle (\sqrt{5}+ \sqrt{2})^2= (3.650)^2= 13.32$, NOT 7.

But $\displaystyle \sqrt{10}$ is approximately 3.162 so $\displaystyle 7+ 2\sqrt{10}= 7+ 2(3.162)= 7+ 6.32= 13.32$ as above.

 

[Acecustis]

Yes, that is wrong. $\displaystyle (a+ b)^2$ is NOT equal to $\displaystyle a^2+ b^2$! Instead $\displaystyle (a+ b)^2= (a+ b)(a+ b)= a(a+ b)+ b(a+ b)$
$\displaystyle = a^2+ ab+ ab+ b^2= a^2+ 2ab+ b^2$ (I'll bet you've seen that before and forgot it!).

$\displaystyle (\sqrt{5}+ \sqrt{2})^2= (\sqrt{5})^2+ 2(\sqrt{5})(\sqrt{2})+ (\sqrt{2})^2$
$\displaystyle = 5+ 2\sqrt{(2)(5)}+ 2= 7+ 2\sqrt{10}$.

As a check, look at the approximate calculator values:
$\displaystyle \sqrt{5}$ is approximately 2.236 and $\displaystyle \sqrt{2}$ is approximately 1.414. $\displaystyle \sqrt{5}+ \sqrt{2}= 2.236+ 1.414= 3.650$ so $\displaystyle (\sqrt{5}+ \sqrt{2})^2= (3.650)^2= 13.32$, NOT 7.

But $\displaystyle \sqrt{10}$ is approximately 3.162 so $\displaystyle 7+ 2\sqrt{10}= 7+ 2(3.162)= 7+ 6.32= 13.32$ as above.

Thanks for the help! I got it now.

 

[sinx]

Please help solve. I'm sure this is simple but I feel like I'm doing something wrong.

(square root of 5 + square root of 2)²


Both numbers are not under one radical but separate radicals (not sure if that matters).

I'm getting 7 for my answer.
Square root of 5 squared = 5
Square root of 2 squared = 2

5+2 = 7

it does matter that the radicals are seperate,
(sqrt5+sqrt2)²=(sqrt5+sqrt2)(sqrt5+sqrt2)

 

[HallsofIvy]

it does matter that the radicals are seperate,
(sgrt5+sqrt2)²=(sgrt5+sqrt2)(sgrt5+sqrt2)

By "separate" do you mean added rather than multiplied: a+ b, rather than ab? Yes, that makes a big difference. $\displaystyle (a+ b)^2$ is not $\displaystyle a^2+ b^2$ but $\displaystyle (ab)^2= a^2b^2$.

 

[mmm4444bot]

… (square root of 5 + square root of 2)²

Hi Acecustis. Here are some notes about notation.

It's standard to text square roots like this: sqrt(x)

Also, we can use a caret symbol to show exponentiation, like this:

[sqrt(5) + sqrt(2)]^2


:idea: There's a link in the forum guidelines to a web site that explains how to type math as text. Check it out! Welcome to the boards. :cool: